Section 57. Each application for a license as an engineer or fireman of a class specified herein or as an operator of hoisting machinery not run by steam shall be made upon a blank furnished by the department, signed and sworn to by the applicant, and shall show the total experience of the applicant. Each such application for a first class engineer’s license, second class engineer’s license or for a special license; for a third class, fourth class or portable class engineer’s license or a steam fire engineer’s license; for a first class or second class fireman’s license; and for a license for operating hoisting machinery not run by steam shall be accompanied by an examination fee to be determined annually by the commissioner of administration under the provision of section three B of chapter seven. Each such application shall entitle the applicant to one examination only, except in case of an appeal under section sixty-six; provided, however, that no person shall make application hereunder for a license of any particular class oftener than once in ninety days. The fee for an examination on appeal shall be determined annually under the aforementioned chapter seven provision.